Since the site is already built you may find it hard to make it fully responsive.

Therefore, you should look to making it adaptive; that is shrink the browser width until it reaches a width where the content won’t fit properly.

This is called a breakpoint and is used with media queries.

Decide how you would like the site to look at lower screen width and then you will have to change the css properties within that media query for some elements on the page to, perhaps, move things around, change sizes etc.